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february_2003 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering McGill University ECSE-221 Introduction to Computer Engineering I Mid Term Exam Examiner: F.P. Ferrie Date: February 14 th , 2003 Question 1 (2 points) A computer uses a 14-bit word for representing signed integers. If the scheme chosen is 2’s complement, then what is the range of numbers represented? Question 2 (2 points) Two 8-bit unsigned integers are multiplied using the algorithm in Assignment 1. If the multiplicand and multiplier are 57 and 71 respectively, then what is the value of the partial product (i.e. sum) at the end of the second iteration? Question 3 (4 points) Encode the number 9.67 x 10 14 using IEEE 754 single precision representation. Express your answer in hexadecimal form. (Compute mantissa to equivalent precision of input.) Question 4 (2 points) A signal with range [-5v,5v] must be sampled with a resolution of 1.0 mV. How many digits would be required to represent this number if a base-5 system were used?
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